Conway circle theorem
E266109
The Conway circle theorem is a geometric result in triangle geometry that identifies a special circle associated with a triangle and certain constructed points, revealing notable collinearities and concyclicity relationships.
All labels observed (1)
| Label | Occurrences |
|---|---|
| Conway circle theorem canonical | 1 |
How this entity was disambiguated
This entity first appeared as the object of triple T2426176 — resolving that mention is where its identity was fixed. The disambiguator weighed these candidate entities and picked the highlighted one (or “None”, minting a new entity). This is how homonymy is resolved: the same surface form can point to different entities.
NED1
Entity disambiguation (via context triple)
gpt-5-mini-2025-08-07
Target entity: Conway circle theorem Context triple: [John H. Conway, hasConcept, Conway circle theorem]
-
A.
de Bruijn–Erdős theorem
The de Bruijn–Erdős theorem is a fundamental result in combinatorics and graph theory that relates finite and infinite structures, notably asserting that certain properties of infinite graphs or set systems are determined by their finite substructures.
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B.
Conway sphere
The Conway sphere is a mathematical construct in knot theory used to decompose knots and links into simpler tangles, named after mathematician John Horton Conway.
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C.
Sperner's lemma
Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
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D.
Euler’s polyhedron formula
Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
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E.
Fermat polygonal number theorem
The Fermat polygonal number theorem is a result in number theory stating that every positive integer can be expressed as a sum of a fixed number of polygonal numbers of a given order.
- F. None of above. chosen
- G. Unsure - the case is ambiguous/there is not enough information to decide.
NED2
Entity disambiguation (via description)
gpt-5-mini-2025-08-07
Target entity: Conway circle theorem Target entity description: The Conway circle theorem is a geometric result in triangle geometry that identifies a special circle associated with a triangle and certain constructed points, revealing notable collinearities and concyclicity relationships.
-
A.
de Bruijn–Erdős theorem
The de Bruijn–Erdős theorem is a fundamental result in combinatorics and graph theory that relates finite and infinite structures, notably asserting that certain properties of infinite graphs or set systems are determined by their finite substructures.
-
B.
Conway sphere
The Conway sphere is a mathematical construct in knot theory used to decompose knots and links into simpler tangles, named after mathematician John Horton Conway.
-
C.
Sperner's lemma
Sperner's lemma is a fundamental result in combinatorial topology that guarantees the existence of a fully labeled simplex in certain labeled triangulations, and is widely used to prove fixed-point and equilibrium theorems.
-
D.
Euler’s polyhedron formula
Euler’s polyhedron formula is a fundamental result in topology and geometry that relates the numbers of vertices, edges, and faces of a convex polyhedron through the equation V − E + F = 2.
-
E.
Fermat polygonal number theorem
The Fermat polygonal number theorem is a result in number theory stating that every positive integer can be expressed as a sum of a fixed number of polygonal numbers of a given order.
- F. None of above. chosen
Statements (30)
| Predicate | Object |
|---|---|
| instanceOf |
geometric theorem
ⓘ
result in triangle geometry ⓘ |
| appliesTo | nondegenerate triangle ⓘ |
| describes |
a special circle associated with a given triangle
ⓘ
collinearity relationships among constructed points of a triangle ⓘ concyclicity relationships among constructed points of a triangle ⓘ |
| field |
Euclidean geometry
ⓘ
geometry ⓘ triangle geometry ⓘ |
| hasProperty |
admits algebraic proofs using barycentric coordinates
ⓘ
admits synthetic geometric proofs ⓘ identifies a canonical circle from side-related constructions ⓘ yields notable point configurations in a triangle ⓘ |
| involves |
circle
ⓘ
collinear points ⓘ concyclic points ⓘ triangle ⓘ |
| namedAfter |
John H. Conway
ⓘ
surface form:
John Horton Conway
|
| namedEntity | true ⓘ |
| relatedTo |
Feuerbach circle
ⓘ
Miquel circle ⓘ Miquel point ⓘ collinearity theorems in triangle geometry ⓘ concyclicity theorems in triangle geometry ⓘ nine-point circle ⓘ |
| usedIn |
advanced olympiad geometry problems
ⓘ
research in triangle centers and configurations ⓘ |
| usesConcept |
barycentric coordinates
ⓘ
cevians ⓘ circle through constructed points ⓘ |
How these facts were elicited
The pipeline generated the facts above by prompting gpt-5.1 with this entity's name + description and the instruction below.
Instruction
You are a knowledge base construction expert. Given a subject entity and a description of it, return factual statements that you know for the subject as a JSON list of dictionaries(triples), where keys must be "subject", "predicate" and "object". The number of facts may be very high, between 25 to 50 or more, for very popular subjects. For less popular subjects, the number of facts can be very low, like 5 or 10. # Requirements - If you don't know the subject at all, return an empty list. - If the subject is not a named entity, return an empty list. - Include at least one triple where predicate is "instanceOf". - Do not get too wordy. - Separate several objects into multiple triples with one object.
Input
Subject: Conway circle theorem Description of subject: The Conway circle theorem is a geometric result in triangle geometry that identifies a special circle associated with a triangle and certain constructed points, revealing notable collinearities and concyclicity relationships.
Referenced by (1)
Full triples — surface form annotated when it differs from this entity's canonical label.
subject surface form:
John H. Conway